Solskjaer's men had fought back to level after conceding two goals in the first nine minutes, only to seemingly see their hopes shattered when Albion substitute Thievy Bifouma scored deep into added time.
But moments later Mats Moller Daehli turned and lashed home Wilfried Zaha's right-wing cross at the other end to send the travelling fans wild.
"We started really, really badly - I have never seen us so pedestrian," Solskjaer told Sky Sports. "We might as well have just sat in with the fans, then maybe we would have woken up quicker.
"But the reaction was magnificent and it says it all about the team and the supporters who sucked the ball in for us."
Solskjaer, no stranger to late drama in his playing career, claimed his side did not deserve to lose the game and applauded their character.
"It was very exciting but I think I've calmed down now," he said.
"I'm so happy for the players and fans that we got the goal we deserved because we did not deserve to lose that game - absolutely no chance.
"We have had a couple of kicks in the teeth lately but we got the luck we don't feel we have had. We have deserved more points from the performances we have had and finally we got the other side of it."
And Solskjaer praised 19-year-old Daehli for showing great composure to slot home at the death, saying: "It's great for him. Mats is going to be a top, top player one day - don't worry about that and I think he deserved his goal. He keeps the ball moving and never gives it away really, but he's not known for scoring goals.
"I've worked with him since June and every single day he does extra (training). It pays off."